Pick over the chickpeas and discard any misshapen beans or stones. Rinse the chickpeas under cold running water and drain. Place in a large bowl with cold water to cover generously and let soak for at least 4 hours or for up to overnight.
Drain the chickpeas, rinse well and transfer to a large saucepan. Add the cold water and bring to a boil over high heat, skimming off the foam that rises to the surface. Reduce the heat to low and simmer, uncovered, until the chickpeas are tender, about 2 hours. Remove from the heat.
In a soup pot over medium-low heat, warm the olive oil. Add the onion, garlic and rosemary sprig and sauté until the onion is softened and translucent but not browned, about 6 minutes. In a small bowl, dissolve the tomato paste in the warm water and add to the pot. Stir in the chickpeas and their cooking liquid and season with salt and pepper. Bring to a simmer over medium heat and cook for 3 minutes. Add the broth, return to a simmer and cook, uncovered, until the flavors have melded, about 30 minutes more. Remove and discard the rosemary sprig.
Working in batches, process the soup in a blender until smooth and creamy and return it to the pot. Alternatively, process the soup in the pot with an immersion blender. Return the soup to a simmer over medium heat, add the farro and cook until the farro is tender yet still slightly firm and chewy, about 25 minutes.
Meanwhile, to prepare the mushrooms, cut away the tips of the mushroom stems. Thinly slice the mushrooms lengthwise. In a large, heavy-bottomed fry pan over medium heat, warm the olive oil. Add the garlic and sauté until fragrant, about 1 minute. Add the mushrooms and cook, stirring with a wooden spoon, until they begin to soften, 3 to 4 minutes. (They might stick to the pan for a moment before beginning to release their juices, but it is not necessary to add more oil.) Raise the heat to high, add the wine and thyme sprig, and cook, stirring constantly, to cook off the alcohol from the wine, about 3 minutes. Reduce the heat to low, season with salt and pepper, and continue to cook, stirring often, until the mushrooms are cooked and their juices have evaporated, about 15 minutes more. Remove from the heat and discard the thyme sprig. Stir in the butter.
Add the mushrooms to the soup and stir to combine. Ladle the soup into warmed soup bowls, garnish with a drizzle of olive oil and a sprinkling of ground pepper and serve immediately. Serves 4 to 6.
Adapted from Williams-Sonoma Essentials of Italian by Michele Scicolone (Oxmoor House, 2007).
